Unifying Views of Tail-Biting Constructions for Linear Block Codes

In this paper, we present new ways of describing and
constructing linear tail-biting trellises for block codes. We extend
the well-known Bahl–Cocke–Jelinek–Raviv (BCJR) construction
for conventional trellises to tail-biting trellises. The BCJR-like labeling
scheme yields a simple specification for the tail-biting trellis
for the dual code, with the dual trellis having the same state-complexity
profile as that of the primal code . Finally, we show that the
algebraic specification of Forney for state spaces of conventional
trellises has a natural extension to tail-biting trellises.